Part 4 The Financial Environment
CHAPTER 8
RISK, RETURN, AND PORTFOLIO THEORY
CHAPTER LEARNING OBJECTIVES
8.1 Distinguish between ex post and ex ante returns and explain how they are estimated.
8.2 Distinguish between arithmetic and geometric means.
8.3 Explain how common risk measures are calculated and what they mean.
8.4 Describe what happens to risk and return when securities are combined in a
8.5 Explain what is meant by the “efficient frontier.”
8.6 Explain what diversification is and why it is important to investors.
8.7 Construct two-security portfolio risk-return frontiers.
Risk, Return, and Portfolio Theory 8 – 2
MULTIPLE CHOICE QUESTIONS
1. Use the following two statements to answer this question:
I. Risk is the possibility of incurring harm.
I. Ex post returns are expected returns while ex ante returns are future returns.
a) I and II are correct.
b) I and II are incorrect.
c) I is correct, II is incorrect.
d) I is incorrect, II is correct.
2. Which of the following is NOT a correct statement about income yield?
a) It is one of the two components of the total return on an investment.
b) It is the return earned in the form of a periodic cash flow received by the investors.
c) These periodic cash flows are interest payments from bonds and dividends from
equities.
d) It measures the periodic cash receipts by dividing it by the selling price of the
security.
3. Which of the following is NOT a true statement?
a) The capital gain yield measures the appreciation in the price of the asset from some
starting price.
b) Common shares should lose from inflation over the long run as their prices and cash
flows are not fixed.
c) The capital loss yield measures the depreciation in the price of the asset from the
purchase price.
d) The addition of the capital gain (or loss) yield explains why the yield gap between
equities and bonds has varied so much over time.
8 – 3 Test Bank for Introduction to Corporate Finance, Fourth Canadian Edition
4. Which of the following is a FALSE statement?
a) Paper losses are capital losses that people accept as losses before they actually sell
and realize
them.
b) A day trader is someone who buys and sells based on intraday price movements.
c) Mark to market refers to carrying securities at the current market value regardless of
whether they are sold or not.
d) The total return including the paper gains and losses over the relevant investment
horizon reflects the economic value of past investment decisions.
5. Which of the following statements is TRUE?
a) The geometric mean measures the average annual rates of return while the
arithmetic mean measures the compound growth rate over multiple time periods.
b) The more the returns vary, the bigger the difference between the arithmetic and
geometric mean will be. The difference is dependent on the relevant investment
horizon.
c) The geometric mean is appropriate when we are trying to estimate the typical return
for a given period.
d) The arithmetic mean is a better average return estimate when we are interested in
the rate of return performance of an investment over time.
6. Melanie bought a share of MPT Company for $53.98 one year ago. The stock paid a
quarterly dividend of $0.52 throughout the year. What is the income yield if the stock is
selling for $57.10 today?
a) 0.91%
b) 0.96%
c) 3.85%
d) 3.64%
7. Laura purchased a share of MVP Company for $26.43 one year ago. The stock paid
a quarterly dividend of $0.50 during the year. What is the capital gain yield if the current
stock price is $28.26?
a) 6.48%
b) 6.92%
c) 7.57%
d) 14.49%
8. Steve bought a share of Toronto Skates Inc. three years ago for $45.00. He was paid
two annual dividends of $4.50 in the past two years. If the stock price today is $ 48.50,
what is the annual holding period return of the stock?
a) 7.78%
b) 15.56%
c) 27.78%
d) 9.26%
8 – 5 Test Bank for Introduction to Corporate Finance, Fourth Canadian Edition
9. Steve bought a share of Toronto Skates Inc. three years ago for $45.00. He was paid
two annual dividends of $4.50 in the past two years. If the stock price today is $ 48.50,
calculate the three year’s income yield, capital gain, and total return.
a) IY=7.78%, CGY=20.00%, TR=27.78%
b) IY=20.00%, CGY=9.26%, TR=29.26%
c) IY=20.00%, CGY=7.78%, TR=27.78%
d) IY=7.78%, CGY=9.26%, TR=17.04%
10. Sandy paid $47.38 for one share of EMH Company one year ago. The stock paid
four quarterly dividends of $1.00 each during the year, and is selling for $49.50 now.
What are the income yield and capital gain yield for EMH over the past year?
a) Income yield = 4.28%; capital gain yield = 8.08%
b) Income yield = 8.08%; capital gain yield = 4.28%
c) Income yield = 4.47%; capital gain yield = 8.44%
d) Income yield = 8.44%; capital gain yield = 4.47%
11. A stock selling for $12.00 today and expected to pay a $1.50 dividend and have a
capital gain of 5% in one year will increase in price to sell at:
a) $ 13.50
b) $ 14.10
c) $ 12.60
d) $ 15.18
12. A stock selling for $20.00 today and expected to have an income (dividend) yield of
3% and a capital gain yield of 5% in one year will increase in price to sell at:
a) $21.60
b) $20.60
c) $21.00
d) $20.40
13. Connie bought 400 shares of ABC Company for $9,288 one year ago. ABC paid a
quarterly dividend of $0.40 per share throughout the year, and is currently trading at
$24.85 per share. What are the income yield, capital gain yield, and total return for
Connie’s investment?
a) Income yield = 6.44%; capital gain yield = 6.56%; total return = 13.00%
b) Income yield = 6.56%; capital gain yield = 6.44%; total return = 13.00%
c) Income yield = 6.89%; capital gain yield = 7.02%; total return = 13.91%
d) Income yield = 7.02%; capital gain yield = 6.89%; total return = 13.91%
14. Suppose you have a total return of 8 percent on the 500 shares of XYZ Company
that you bought for $9,590 last year. XYZ paid four equal quarterly dividends during the
year. What would be the quarterly dividend if the current stock price is $18.64 per
share?
a) $0.50
b) $0.52
c) $0.54
d) $0.56
15. You made an investment in your RRSP account of $3,000 in an ETF that pays
quarterly dividends. The price of each unit the day of the investment is $60. The
following year you invested another $2,000 in your RRSP account at a price of $ 70 a
unit. How much would you have in your account two years after your initial investment if
you know that the income yield of the ETF is 5% and an ETF unit is trading at $75
today?
a) $6500.00
b) $6292.86
c) $5992.86
d) $6042.86
Risk, Return, and Portfolio Theory 8 – 8
16. The capital gain yield of an equity security is 9.27 percent. The security paid a
quarterly dividend of $0.55 per share during the year. What is the current price of the
security if the total return is 13.76 percent?
a) $12.25
b) $13.38
c) $49.00
d) $53.54
17. A year ago, you bought some shares of CIA Company, which pays equal quarterly
dividends. The income yield and the capital gain yield are 4.38 percent and 9.5 percent,
respectively. The current price of CIA is $18. What was the quarterly dividend that CIA
paid during the year?
a) $0.18
b) $0.41
c) $0.72
d) $1.64
18. A share of Oedipus Construction Company was selling for $32.16 one year ago.
The stock paid an annual dividend of $0.25 during the year. What is the capital gain
yield if the current stock price is $34.02?
a) 9.45%
b) 5.78%
c) 7.77%
d) 5.46%
19. In question 18 above, what is the income yield (dividend yield) for the stock of
Oedipus Construction Company?
a) 0.945%
b) 0.578%
c) 0.777%
d) 0.546%
20. The income yield and capital gain yield of a stock are 4.90 percent and 7.37
percent, respectively. The stock paid a quarterly dividend of $0.65 per share during the
year. What should the stock sell for today?
a) $35.28
b) $37.01
c) $53.06
d) $56.97
21. The following table shows the closing prices and daily returns of Toronto Skates Inc.
over a week:
Day Closing Price Returns
Monday 35.20 1.15%
Tuesday 34.90 -0.85%
Wednesday 37.00 6.02%
Thursday 35.00 -5.41%
Friday 35.10 0.29%
Risk, Return, and Portfolio Theory 8 – 10
Calculate the weekly geometric and arithmetic returns of Toronto Skates Inc. (your
answer should be four decimals, margin of error is +/- 0.0050%)
a) GM=0.2400% and AM=0.1728%
b) GM=-0.2841% and AM=0.1728%
c) GM=0.1728% and AM=-0.2841%
d) GM=0.1728% and AM=0.2400%
22. La Maudite Corporation’s annual returns for the past five years were: 11.5%, 18%, –
12%, -16.5%, and 28%. What are the arithmetic and geometric average annual returns
for La Maudite over the five-year period?
a) Arithmetic mean = 5.80%; geometric mean = 4.35%
b) Arithmetic mean = 4.35%; geometric mean = 5.80%
c) Arithmetic mean = 17.20%; geometric mean = 17.05%
d) Arithmetic mean = 17.05%; geometric mean = 17.20%
23. You have observed the following for Montreal Smoked Meat Corporation:
Closing Price
May 4, 2016 $25.09
May 11, 2016 $26.37
May 18, 2016 $25.68
May 25, 2016 $26.95
June 1, 2016 $27.50
June 8, 2016 $26.77
June 15, 2016 $27.45
8 – 11 Test Bank for Introduction to Corporate Finance, Fourth Canadian Edition
What are the arithmetic and geometric average weekly returns over the 6-week period
ended June 15, 2016?
a) Arithmetic mean = 3.317%; geometric mean = 3.309%
b) Arithmetic mean = 3.309%; geometric mean = 3.317%
c) Arithmetic mean = 1.559%; geometric mean = 1.509%
d) Arithmetic mean = 1.510%; geometric mean = 1.559%
24. The geometric average quarterly return of ROM Company was 5 percent for the
previous year. What was the return for the third quarter if the returns for the first,
second, and fourth quarters were 10 percent, -9.05 percent, and 8 percent,
respectively?
a) –6.18%
b) –7.05%
c) 11.05%
d) 12.50%
25. The geometric average daily return for Grumpy Inc. was 3 percent for this past
week. Grumpy’s stock was traded at $18.82 when the market closed on Friday. The
daily returns for Monday through Thursday are 5 percent, 2 percent, -10 percent, and 8
percent, respectively. What is the opening price of Grumpy on Friday?
a) $16.68
b) $16.90
c) $16.94
d) $17.11
Risk, Return, and Portfolio Theory 8 – 12
26. The arithmetic average daily return for Dopey Inc. was 2 percent for this past week.
Dopey’s stock was traded at $23.70 when the market closed on Friday. The daily
returns for Monday, Tuesday, Thursday, and Friday are 4.8%, 5.6%, -4.0%, and 12.2%,
respectively. What was Dopey’s opening price on Monday?
a) $21.47
b) $21.55
c) $21.75
d) $22.80
27. Baxter Inc.’s annual returns for the past four years were: 2.75%, -1.8%, 7.2%, and
6.5%. What are the arithmetic and geometric average annual returns for Baxter over
the four-year period?
a) Arithmetic mean = 6.80%; geometric mean = 3.35%
b) Arithmetic mean = 3.66%; geometric mean = 3.60%
c) Arithmetic mean = 14.65%; geometric mean = 10.05%
d) Arithmetic mean = 18.03%; geometric mean = 21.20%
28. AMC Corp had a geometric weekly return of 5% for this past week. The daily returns
for Monday through Thursday are 4 percent, 3 percent, -7 percent, and 9 percent,
respectively. If AMC’s stock traded at $16.22 when the market closed on Friday, what is
the opening price of the stock on Friday?
a) $13.47
b) $13.38
c) $13.94
d) $14.11
29. What is the expected return on a stock that has a 15 percent probability of a 35
percent return, a 20 percent probability of a 25 percent return, a 50 percent probability
of a 15 percent, and a probability of 15 percent of –20 percent?
a) 18.75%
b) 14.75%
c) 13.75%
d) 20.75%
30. What is the expected return from an investment that has an equally likely probability
to lose half of the investment or double the investment?
a) 50%
b) 125%
c) –50%
d) 200%
31. You have done a thorough study of the economy and of Stock X and concluded the
following probabilities: having a boom next year is 20 percent, having a stable economy
is 55 percent, and having a recession is 25 percent. You have also found the price of
Stock X will be: $45 if there is a boom, $25 if the economy is stable, and $15 if there is a
recession. What is the ex ante expected return on Stock X if it is currently selling for
$24?
a) –9.43%
b) 10.42%
c) 18.06%
d) 26.50%
32. Given the information in the following table, what is the expected return of the
security?
State of the Economy Probability of Occurrence Expected
Return
High Growth 10% 35%
Moderate Growth 25% 20%
No Growth 50% 10%
Recession 15% –15%
a) 11.25%
b) 12.50%
c) 15.75%
d) 25.00%
33. If the closing price of Stock Y was $38.63 on Friday, which was after it had earned
daily returns of 8 percent, 23 percent, -30 percent, 20 percent, and -5 percent during the
week (Monday to Friday), what was the opening price of Stock Y on Monday?
a) $17.47
b) $17.75
c) $33.00
d) $36.44
34. On January 1, you forecasted that there is a 45 percent chance that the stock price
of Edward Bear Inc. will be $95 in one year while there is a 55 percent chance that the
stock price will be $35. Six months later, you revised the estimated probability to 25
percent chance of the high state (stock price of $95). If the market agrees with your
revised forecasts, what is the expected change in stock price from January 1 to July 1?
Assume the discount rate is zero.
a) Price goes up by 19.35%
b) Price goes down by 19.35%
c) Price goes up by 24%
d) Price goes down by 24%
35. Which of the following statements is TRUE?
a) The more stable the possible returns, the greater the risk.
b) Risk means the probability that the actual return from an investment is less than the
expected return.
c) The range is a more accurate measure of risk than the standard deviation, because
the range uses the maximum and minimum values, whereas the standard deviation
uses all the observations.
d) Securities offering lower expected rates of return tend to be riskier.
36. Which of the following statements is FALSE?
a) Risk measures the volatility of the returns of the asset.
b) Risk measures are concerned only with the negative performance of the asset.
c) The standard deviation is not the only measure of risk.
d) Risk and return are inversely related.
37. You have observed the following annual returns for Motherboard Inc.: 25%, 15%, –
20%, 30%, and -15%. What are the variance and standard deviation of returns?
a) Variance = 0.00425; standard deviation = 0.06519
b) Variance = 0.06519; standard deviation = 0.00425
c) Variance = 0.05325; standard deviation = 0.23076
d) Variance = 0.23076; standard deviation = 0.05325
8 – 17 Test Bank for Introduction to Corporate Finance, Fourth Canadian Edition
38. The closing prices for Stock B from December to June are: $42.90, $44.20, $51.50,
$49.60, $45.50, $46.30, and $42.50. What is the standard deviation of returns over the
six-month period?
a) 0.295%
b) 0.868%
c) 5.436%
d) 9.318%
39. What is the standard deviation of returns on a stock priced today at $10 that has a
25 percent probability of increasing to $13, a 50 percent probability of increasing to $12,
a 15 percent probability of increasing by 5 percent, and a 10 percent probability of
decreasing to $ 7?
a) 0.0094
b) 0.0286
c) 0.0968
d) 0.1692
40. Given the following forecasts, what is the standard deviation of returns?
State of the Economy Probability of Occurrence Expected
Return
Expansion 25% 45%
Normal 60% 20%
Recession 15% –15%
a) 18.4120%
b) 11.3908%
c) 3.3900%
d) 1.2975%
41. Given the following forecasts, what is the variance of returns?
State of the Economy Probability of Occurrence Expected
Return
Expansion 25% 45%
Normal 60% 20%
Recession 15% –15%
a) 18.4120% squared
b) 11.3908% squared
c) 3.3900% squared
d) 1.2975% squared
42. You have given the following forecasts for the economy and Stock A: (1) the
probability of having a recession next year is 30 percent, a normal economy is 55
percent, and an expansion is 15 percent, and (2) the price of Stock A will be $9 if the
economy is in recession, $15 if the economy is normal, and $18 if the economy is in
expansion. What is the ex ante standard deviation of Stock A’s returns if it is currently
selling for $12?
a) 7.1719%
b) 26.7804%
c) 29.4219%
d) 54.2419%
43. You have been given the following forecasts for the economy and Stock A: (1) the
probability of having a recession next year is 30 percent, a normal economy is 55
percent, and an expansion is 15 percent, and (2) the price of Stock A will be $9 if the
economy is in recession, $15 if the economy is normal, and $18 if the economy is in
expansion. What is the ex ante variance of Stock A’s returns if it is currently selling for
$12?
a) 7.1719%2
b) 26.7804%2
c) 29.4219%2
d) 54.2419%2
44. Which of the following statements is FALSE?
a) The standard deviation is one measure of risk.
b) Risk measures focus only on the negative performance of the asset.
c) The volatility of the returns of the asset is a measure of risk.
d) Risk increases as return decreases.
45. Aquarius Inc. has posted the following annual returns for the past 5 years: 17%,
23%, -13%, 7%, and -15%. What are the variance and standard deviation of these
annual returns?
a) Variance = 0.00237; standard deviation = 0.04868
b) Variance = 0.06221; standard deviation = 0.2494
c) Variance = 0.02972; standard deviation = 0.1724
d) Variance = 0.2341; standard deviation = 0.4838
46. Which of the following is a TRUE statement of modern portfolio theory?
a) It states that securities should be managed within a portfolio, rather than individually,
to lower risk-reduction gains.